Related papers: Ordinal pattern dependence and multivariate measur…
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects.…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative)…
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a…
We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
We introduce Ordinal Synchronization ($OS$) as a new measure to quantify synchronization between dynamical systems. $OS$ is calculated from the extraction of the ordinal patterns related to two time series, their transformation into…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
We propose a nonparametric test of spatial independence for data observed on irregular, non-lattice point clouds $\mathcal{V}_{n}\subset\mathbb{R}^{2}$. For each location $v\in\mathcal{V}_{n}$, we encode the local spatial configuration…
In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…
Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to…
A regression model is proposed for the analysis of an ordinal response variable depending on a set of multiple covariates containing ordinal and potentially other variables. The proportional odds model (McCullagh (1980)) is used for the…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…